Problem: Every bag of Dummies (a chocolate candy) contains the same number of pieces.

The Dummies in one bag can't be divided equally among $9$ kids, because after each kid gets the same (whole) number of pieces, $7$ pieces are left over.

If the Dummies in three bags are divided equally among $9$ kids, what is the smallest number of pieces that could possibly be left over?
Let $n$ be the number of Dummies in one bag. Then we know $n\equiv 7\pmod 9$, so $$3n\equiv 3(7) = 21\equiv 3\pmod 9.$$Thus, when the Dummies in three bags are divided equally among $9$ kids, there is a remainder of $\boxed{3}$ leftover pieces.

We can also explain this solution without using modular arithmetic. Each bag can be divided equally among the $9$ kids with $7$ pieces from each bag left over. This makes $21$ leftover pieces, which are enough to give each kid $2$ more candies and have $3$ candies left over. Those last $3$ candies can't be divided equally among the kids, so the answer is $\boxed{3}$.